On the Generalization and Decomposition of the Bonferroni Index

OPHI Working Papers

A simple algorithm is proposed which defines the Bonferroni index as the product of a row vector of individual population shares, a linear mathematical operator called the Bonferroni matrix and a column vector of income shares. This algorithm greatly simplifies the decomposition of the Bonferroni index by income sources or classes and population subgroups. The proposed algorithm also links the Bonferroni index to the concepts of relative deprivation and social welfare and leads to a generalization where the traditional Bonferroni and Gini indices are special cases. The paper ends with an empirical illustration based on EU-SILC data for the year 2008. 

Citation: Bárcena-Martin, E. and Silber, J. (2012). 'On the generalization and decomposition of the Bonferroni Index', OPHI Working Papers 51, Oxford Poverty and Human Development Initiative (OPHI), University of Oxford.

This paper is also published in Social Choice and Welfare, 2013, Vol. 41(4), pp. 763–787.

Gini, inequality decomposition, population subgroups, relative deprivation, social welfare, EU-SILC
Europe and Central Asia

Elena Bárcena-Martin and Jacques Silber
Series Name
OPHI Working Papers
Publication date
JEL Codes
D31, D63
Publication Number
WP 51